GCF of 320/71, 360/6966
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 320/71, 360/6966 i.e 40/494586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 320/71, 360/6966.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 320/71,360/6966?
Given fractions are 320/71,360/6966
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 320/71,360/6966, numerators are 320,360
Denominators are 71,6966
The GCF of 320,360 is 40 .
LCM of 71,6966 is 494586.
The greatest common factor of 320/71,360/6966 = [GCF of 320,360]/[LCM of 71,6966]= 40/494586
Therefore, the GCF of 320/71,360/6966 is 40/494586.
To find the highest common factor of 320,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 320,360 is 40.
Lets's calculate GCF of 320,360
| 2 | 320, 360 |
| 2 | 160, 180 |
| 2 | 80, 90 |
| 5 | 40, 45 |
| 8, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 320,360 By Matching Biggest Common Factor Method
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 320,360 . The biggest common factor number is the GCF number.
So the greatest common factor 320,360 is 40.
Lets's calculate LCM of 71,6966
Given numbers has no common factors except 1. So, there LCM is their product i.e 494586
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/494586
Therefore, the GCF of Fractions 320/71,360/6966 is 40/494586
Least Common Multiple of 71,6966 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 71,6966 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,6966) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,6966) x common factors =1 x 1 = 1
LCM(71,6966) = ( 71 × 6966 ) / 1
LCM(71,6966) = 494586 / 1
LCM(71,6966) = 494586
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 320/71, 360/6966
1. What is the HCF of 320,360?
The HCF of 320,360 is 40
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 320/71, 360/6966?
Answer: GCF of Numerators as per given numbers 320/71, 360/6966 is
GCF of Numerators i.e. for 320,360 is 40
LCM of denominators i.e. for 71,6966 is 494586.
Thus, GCF of Fractions is 40/494586.Finally, GCF of Fractions for 320/71, 360/6966 is 40/494586.